Prediction of thermal conductivity of nanostructures: Influence of phonon dispersion approximation

In this study, the influence of phonon dispersion approximation on the prediction of in-plane and out-of-plane thermal conductivity of thin films and nanowires is shown. Results obtained using the famous Holland dispersion approximation and the Brillouin zone boundary condition (BZBC) dispersion curves are compared. For (in-plane and out-of-plane) thermal conductivity predictions based on BZBC dispersion curves, new relaxation time parameters fitted from experimental data of bulk silicon thermal conductivity are reported. The in-plane thermal conductivity of nanostructures (films of thicknesses 20 nm, 100 nm, and 420 nm and nanowires of widths 22 nm, 37 nm, and 100 nm) in the temperature range 20–1000 K is calculated from the modified bulk thermal conductivity model by scaling the bulk phonon mean free path (MFP) by the Fuch–Sondheimer factor of boundary scattering developed for nanostructures with rectangular cross-section. The pseudo out-of-plane thermal conductivity of films of thicknesses 20 nm, 100 nm, and 420 nm and in the temperature range 150–1000 K is calculated from the solution of the Boltzmann transport equation (BTE) for phonons by using the Discrete ordinate method (DOM), and the Monte Carlo (MC) simulation. In order to confirm the current results, the calculated in-plane thermal conductivity of silicon thin films and silicon nanowires are compared with existing experimental data. Moreover, due to lack of experimental and theoretical data of out-of-plane thermal conductivity of thin films, comparison of the DOM and MC simulation is performed. The current work shows that a drastic simplification of dispersion curves can lead to wrong prediction of both in-plane and out-of-plane thermal conductivities of nanostructures, especially for ultra thin nanostructures and/or at high temperatures. Comparison with experimental data of in-plane thermal conductivity of silicon thin films and silicon nanowires proves that more refined dispersion approximation such as the BZBC is well adequate for phonon transport calculations when confinement has negligible effect. Moreover, the comparison between the thermal conductivity in the out-of-plane direction and that in the in-plane direction enables one to quantify the anisotropy of thermal conductivity of the film.